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Australian Prime Minister Malcolm Turnbull on Thursday made his first visit to Indonesia since taking power, seeking to repair a key relationship strained by repeated crises under his conservative predecessor.

Ties between the neighbors sank to their lowest level in years under former premier Tony Abbott, over rows about Jakarta's execution of Australian drug smugglers, Canberra's hardline policy of turning migrant boats back to Indonesia and espionage allegations.

Hopes are high that relations will improve under Turnbull, who took power in a Liberal Party coup in September. His views are more socially liberal than Abbott, whose tough approach often riled Jakarta.

Despite signs of warming relations, Turnbull's government has shown no signal of easing its tough immigration laws and the controversial policy of turning back boats from its shores remains a source of tension.

Arriving in Jakarta, Turnbull signaled he would try to keep the focus of the one-day visit firmly on economic ties, saying he and Indonesian President Joko Widodo were "both businessmen that got into politics".

"Trade, investment, economic growth, stronger economies -- in both Indonesia and Australia for the benefit of both sides -- is the focus of the discussions," he told reporters in Jakarta, before heading to the presidential palace for talks with Widodo.

The allies are key trade partners, with Indonesia a major market for Australian exports, including cattle and wheat. Australian Trade Minister Andrew Robb is set to lead a large delegation of Australian business leaders to Indonesia next week.

Jakarta and Canberra work together in a number of other areas, including combating Muslim extremism. Fears are growing in both Muslim-majority Indonesia and Australia that their nationals who have fought with the Islamic State group in the Middle East could launch attacks on home soil.

It is Turnbull's second foreign visit since taking power -- his first was to New Zealand -- and he will go on afterwards to several international summits.

String of crises

Despite the long-standing ties, under Abbott's leadership the relationship sank to its worst level since 1999 when Australia sent troops to East Timor as part of an international peacekeeping force to stem bloodshed after the territory voted for independence from Indonesia.

Tensions peaked in April when Jakarta put to death two Australian drug traffickers, Andrew Chan and Myuran Sukumaran, despite repeated appeals from Canberra for mercy. Australia took the unprecedented step of recalling its ambassador from Jakarta for several weeks following the executions.

Indonesia has also been angered by Canberra's hardline immigration policies, which are aimed at stopping the flow of asylum-seeker boats to Australia and include turning vessels back to Indonesia -- a key transit point for migrants -- when it is safe to do so.

The issue blew up again in June when Australian officials were accused of paying people-smugglers heading to New Zealand $31,000 to take asylum-seekers back to Indonesia.

The relationship was rocky from the early days of Abbott's premiership. A row erupted in 2013, shortly after he took power, over allegations Australian spies tried to tap the phone of then Indonesian president Susilo Bambang Yudhoyono several years earlier.

Despite the recent rockiness, there have been signs the relationship is getting back on track.

Visits by Australian ministers -- which were frozen following the executions -- have resumed in recent months, while Indonesia's ambassador to Australia, Nadjib Riphat Kesoema, said this week the neighbors were again enjoying "very good relations".